Question

Provide step-by-step solutions to the given problem below. Write your answers on

the spaces provided.

Consider all samples of size 2 from the population 2, 5, 6, 9, 11, and 13. Compute

the mean, and variance of the sampling distribution of the sample mean.

First step:

Second step

a)

b)

Third step

Fourth step

Fifth step

Sixth step

a)

b)

Seventh step

a)

b)

c)

d)

Answer 1

$The\,\,mean\,\,is\,\,\\\mu =\frac{23}{3}\\The\,\,variance\,\,is\\\sigma ^2=\frac{\sum{{\bar{x}_i}^2}}{15}-\mu ^2=\\=\frac{3.5^2+4^2+2\cdot 5.5^2+6.5^2+7^2+2\cdot 7.5^2+8^2+8.5^2+9^2+9.5^2+10^2+11^2+12^2}{15}-\left( \frac{23}{3} \right) ^2=\\=\frac{50}{9}$